Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-4y &= -1 \\ -7x-8y &= -5\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-8y = 7x-5$ Divide both sides by $-8$ to isolate $y$ $y = {-\dfrac{7}{8}x + \dfrac{5}{8}}$ Substitute this expression for $y$ in the first equation. $-x-4({-\dfrac{7}{8}x + \dfrac{5}{8}}) = -1$ $-x + \dfrac{7}{2}x - \dfrac{5}{2} = -1$ Simplify by combining terms, then solve for $x$ $\dfrac{5}{2}x - \dfrac{5}{2} = -1$ $\dfrac{5}{2}x = \dfrac{3}{2}$ $x = \dfrac{3}{5}$ Substitute $\dfrac{3}{5}$ for $x$ back into the top equation. $- \dfrac{3}{5}-4y = -1$ $-\dfrac{3}{5}-4y = -1$ $-4y = -\dfrac{2}{5}$ $y = \dfrac{1}{10}$ The solution is $\enspace x = \dfrac{3}{5}, \enspace y = \dfrac{1}{10}$.